The electric field and ion current distribution on the ground level and corona losses are the important factors for designing high-voltage direct current (HVDC) transmission lines. This study presents a new finite-difference-based flux tracing (FDFT) method for analysing the ionised field. The differential equations are discretised using the finite-difference method and the non-linear algebraic equations are constructed. For the bipolar field, a systematic technique to set up the initial values is well established by estimating the average values of space charge density. The issues of the finite-difference scheme, the normalisation and the selection of mesh points are elaborately discussed to have a better convergence. The boundary conditions of the ionised field equations can be enforced directly, whose benefit is that the iterative process to satisfy the boundary conditions can be completely avoided. The numerical examples show that the results obtained in this study agree well with the ones published in other literatures. The FDFT could be applied for more complicated line configuration with unequal corona-onset electric fields and ion mobilities of opposite polarities.

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